O.K. . I only have 30 min. for lunch,
The purpose of the comp. nut is supposedly for being able to ensure that playing chords up and down the fretboard are more uniformly in tune. Yes/No? edit : (and play against a keyboard?)
To challenge this, last night I intonated my $300 Stagg Les Paul copy.edit

And tuned it Standard 440 A), I played the simple M7 barre chord, from the open position ,all the way up in half steps til the EM7 at the 12 fret.
I paid close attention to the pressure exerted while playing the chords, I let them sustain.
The end result was the chords were perfectly in tune ALL the way up. There was ZERO oscillation in the playing of the chords. Period.
I'm out of time and will come back to this thread later today.sorry
EDIT:
also, lastnight I did earvana's test - tune low E string,then play that same string up to E#,F,G,G#,A. You should notice that the sting goes out of tune per earvana - * my tuner tracked that the notes were in tune !
also they state that playing an open EM7 chord to a D chord (1st position) you'll notice a difference in it being out of tune - * I did'nt notice any, both chords sounded totally in tune from one to the other !
some facts from wiki:
the interval of one cent is much too small to be heard between successive notes.
(the interval between two adjacent piano keys) is equal to 100 cents.
The just noticeable difference for this unit is about 6 cents.
It is difficult to establish how many cents are perceptible to humans; this accuracy varies greatly from person to person.
One author stated that humans can distinguish a difference in pitch of about 5-6 cents.
I'll be back a little later...
last edit -
per Earvana " a typical guitar is +4 cents sharp/-2 cents flat . . .
and wiki-The just noticeable difference for this unit is about 6 cents. :dontknow: